On the holographic renormalization group

@article{Boer1999OnTH,
  title={On the holographic renormalization group},
  author={Jan de Boer and Erik P. Verlinde and Herman L. Verlinde},
  journal={Journal of High Energy Physics},
  year={1999},
  volume={0008},
  pages={003-024}
}
We propose a direct correspondence between the classical evolution equations of $5-d$ supergravity and the renormalization group (RG) equations of the dual $4-d$ large $N$ gauge theory. Using standard Hamilton-Jacobi theory, we derive first order flow equations for the classical supergravity action $S$, that take the usual form of the Callan-Symanzik equations, including the corrections due to the conformal anomaly. This result gives direct support for the identification of $S$ with the quantum… 
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